TY - JOUR
T1 - A mapping theorem for topological complexity
AU - Grant, Mark
AU - Lupton, Gregory M
AU - Oprea, John F
PY - 2015/6/19
Y1 - 2015/6/19
N2 - We give new lower bounds for the (higher) topological complexity of a space in terms of the Lusternik–Schnirelmann category of a certain auxiliary space. We also give new lower bounds for the rational topological complexity of a space, and more generally for the rational sectional category of a map, in terms of the rational category of a certain auxiliary space. We use our results to deduce consequences for the global (rational) homotopy structure of simply connected hyperbolic finite complexes.
AB - We give new lower bounds for the (higher) topological complexity of a space in terms of the Lusternik–Schnirelmann category of a certain auxiliary space. We also give new lower bounds for the rational topological complexity of a space, and more generally for the rational sectional category of a map, in terms of the rational category of a certain auxiliary space. We use our results to deduce consequences for the global (rational) homotopy structure of simply connected hyperbolic finite complexes.
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U2 - 10.2140/agt.2015.15.1643
DO - 10.2140/agt.2015.15.1643
M3 - Article
SN - 1472-2747
VL - 15
SP - 1643
EP - 1666
JO - Algebraic and Geometric Topology
JF - Algebraic and Geometric Topology
IS - 3
ER -